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I usually use terms like 'radiowave', 'microwave', 'X-ray', etc. to refer to ranges of electromagnetic (EM) frequencies ($f=2\pi/\omega$) or wavelengths ($\lambda = 2\pi/k$) in air or in a vacuum, where the speed of propagation is approximately the same as the speed of light in vacuum ($v\approx c$) and the dispersion relation is $\omega = c k\,$. In matter however, $f(\lambda)$ is different than in a vacuum (e.g. for the Drude metal, $\omega = (c^2 k^2+ \omega_p^2)^{1/2}$, with plasma frequency $\omega_p$).

In the literature (or on wikipedia, for different languages), terms like 'ultraviolet' sometimes seem to refer to wavelength ranges and other times to frequency ranges. For the vacuum EM spectrum, there is a fixed correspondence, thus there is no ambiguity.

When referring to EM waves in matter, do physicists stick to using the same terms (e.g. 'ultraviolet') to refer to the same exact numerical values for the ranges of frequency and wavelength, as defined for the vacuum EM spectrum? In that case, whatever numerical value one has for $f$ or $\lambda$ (even for waves in matter), these values could still be referred to as in the 'visible', 'ultraviolet', 'microwave' range etc., even though the described EM wave has a different dispersion relation as a vacuum EM wave.

Maybe it's just me, but it seems wrong to constantly be using the vacuum dispersion relation to convert wavelengths into frequencies or the other way around (e.g. when the terms 'visible', 'ultraviolet', etc. are used in some piece of literature), when one is actually concerned with describing waves with a different dispersion relation.

This confusion makes it a little bit difficult to understand some texts like [Mori, Electronic Properties of Organic Conductors, 2016, p. 120].

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  • $\begingroup$ Aren't you confusing things? EM waves are characterized by their frequency, which is independent of material (although you then calculate $\omega(k)$, because its more naturally arising from theory, but the frequency is "unchanging"). $\lambda$ and hence $k$ change inside materials, and the interaction is always in function of $\omega$. The interaction can always be defined by a complex term, dependent on $\omega$. And yes, physicists always talk about frequency and, if a name is given, vacuum wavelength, because we cannot measure it inside materials. But frequency does not change! $\endgroup$ May 31, 2020 at 13:06
  • $\begingroup$ for example, the plasma frequency eq you posted, can be solved for $\omega$. And that frequency is the same in vacuum and in your material. ie. that relationship is the one you will find if you shine an EM field with (vacuum) $\omega$ there. It remains unchanged for that relationship. $\endgroup$ May 31, 2020 at 13:08
  • $\begingroup$ $k$ changes though... $\endgroup$ May 31, 2020 at 13:08
  • $\begingroup$ Another way to remember this is that $E=\hbar\omega$. Then you see that its energy/frequency is what defines the name and then vacuum wavelength. $\endgroup$ May 31, 2020 at 13:18

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The division of the EM spectrum into spectral regions is independent of the medium - but when the medium has a dispersion relation that differs from vacuum significantly enough to make a difference, the classification is done in terms of frequency (which is the same in every medium) instead of wavelength (which, as you noted, doesn't).

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